Social networks

OpenProf

Unlock access to content

Select one option:

Free of charge

Unlock the chapter "Straight Line Graphs"

Unlock access to the solution of problems in this chapter.
Free of charge Price: 3.00 £

Continue »

Subscribe to OpenProf If you do not get a better grade, you get your money back!

Unlock access to all problems solutions.
Available from 8.25 £ / month.

Continue »

mathematics UK Year 10 Mathematics (KS4)

Solved problems for the chapter:

Straight Line Graphs

View the theory »

Equation of a straight line for KS4

0.1. The Gradient-Intercept Form:

0.2. The General Form:

0.3. The intercept form of the equation of a line:

1. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:straight_line_graphs/3576/

Example 1.

Given the points , , and , determine which of the points lie on line .

Example 2.

Obtain the point which lies on line and have abscissa 2.

Obtain the point which lies on line and have abscissa 0:

Obtain the point which lies on line and have abscissa .

Obtain the point lying on the line and having an abscissa .

Obtain the point which lies on line and have ordinate .

Obtain the point which lies on line and have ordinate 10.

Obtain the point which lies on line and have ordinate .

10.

Obtain the slope-intercept form of the equation of a straight line whose gradient is 2 and the point T(2,1) lies on it.

11.

Given the line .

For , calculate the zero of the function and the intersection of the graph with the ordinate axis.
Calculate the value of m given that the graph of the function is parallel to the line .

12.

Obtain the slope-intercept form of the equation of a straight line whose gradient is —3 and the point T(1,2) lies on it.

13.

Obtain the slope-intercept form of the equation of a straight line whose gradient is and the point T(4,0) lies on it.

14.

Obtain the equation of the line passing through the points (-3, -1) and (0,5).

15.

Obtain the slope-intercept form of the equation of a straight line whose gradient is and the point lies on it.

16.

Obtain the slope-intercept equation of the line passing through the points (1,5) and (6, -10).

17.

Obtain the slope-intercept form of the equation of the line passing through the points (1, -1) and (-3,1).

18.

Obtain the slope-intercept form of the equation of the line passing through the points and .

19.

Prove that the points A(4,5), B(-8,2) and C(44,15) lie on the same line.

20.

The point lies on the line p, which is parallel to the bisectors of the odd quadrants. Obtain in slope-intercept form, the equation of the line p.

21.

Obtain the equation of the line function f which intersects the ordinate axis at and f(7) = 1.

22.

The graph of the linear function f(x) passes through the points A(- 3, 5) and B(3, -1). Write down the relation of this function.

23.

Given that f(4) =1, f(-2)=4 and f(x) is a linear function. Obtain the relation of the function f(x).

24.

Obtain the slope-intercept form of the line parallel to the line and goes through the point T(-4,7).

25.

Obtain the linear function f such that f(2)=0 and the intersects on the y-axis is at the point (0,-4).

26.

Write a rule for the linear function f whose graph intersects the abscissa axis at -8 and the ordinate axis at 4.

27.

The graph of the function f is parallel to the abscissa axis and goes through the point . Obtain the the relation for the function f.

28.

Given a triangle with vertices , and

Obtain the equation of the line joining the points A and B.
Obtain the equation of the line passing through the vertex C and parallel to the side AB.
Obtain the equation of the line connecting the centroid and the side AB.

29.

Obtain the general form of the line passing through the point and parallel to the line

30.

Obtain the general form of the line passing through the points and

31.

Obtain the general form of the equation of the line passing through the points and

32.

Obtain the general form of the line .

33.

Obtain the intercept form of the line passing through the points and . Also plot its line.

34.

Obtain the intercept form of the line passing through the points and . Also, plot its graph.

35.

Obtain the intercept form of the line passing through the points and . Also, plot the

graph of the line.

36.

Obtain the intercept form of the line passing through the point and is parallel to the line .

37.

Obtain the intercept form of the line passing through the point and parallel to the line Also, plot the line.

38.

Obtain the gradient of the line given by the equation .
Plot the graph of the given line.
Calculate the area of the triangle bounded by the line and the coordinate axes.

39.

Given the line obtain the gradient-intercept form and intercept form of the line.

40.

Obtain the equation of the line below in all three forms.

41.

Obtain three forms of the equation of the line passing through the points and

42.

Obtain the three forms of the equation of the line passing through the point and is parallel to the line

43.

Determine the possible value(s) of for which the line can be written in:

general form,
gradient-intercept form.

44.

Given the equation of the line , find the possible values of for which the line:

is parallel to the line ,
can be written in the intercept form,
intersects the x- axis at point .

45.

Obtain the gradient-intercept form of the equation of the line through points A (2, -3) and B (-4, -6).
Calculate the area of the triangle between the line and the coordinate axes.

46.

In the given coordinate system, mark the points A (0, 5) and B (10, 0) and draw a line through them.
Obtain the equation of the line.
Calculate ABO ( O is the origin of the axes ). Express your answer to the nearest minutes.

47.

The vertices of a triangle ABC are , , .

Calculate the area of the triangle.
Obtain three forms of the equation of the line passing through the points A and B.
Find the points intersection of the line AB with the coordinate axes.

48.

Given a triangle ABC with vertices , and C lying on the line , calculate the vertex C if area of the triangle ABC is 12.5 sq. unit.

49.

The tangent to the curve at a point is perpendicular to the line . Find the value of the real number a.

50.

In the coordinate system, parallel lines and are drawn. The line passes through the point . Complete the table below using the given information.

Line	Line


Equation of line :	Equation of line :

51.

Plot the graph of the line in the given coordinate system.
Locate the point A with the ordinate - 1 on the line drawn above. Obtain the abscissa of the point A.
Calculate how far the point A is from the origin of the coordinate system. Leave your answer in surd form.

52.

Obtain the equation of straight line passing through points and .

53.

Given the graph below.

Obtain the coordinates of the points A, B and C and calculate the distance between the points A and C.
Obtain the equation of the straight line through the points B and C.
Calculate the size of the angle .

54.

Obtain the equation of the line parallel to the line and intersects the ordinate axis at the point . Draw both lines in the given coordinate system.