 New Zealand
Level 6 - NCEA Level 1

Equations of Lines (Mixed Set)

Lesson

We have now looked at a number of ways of finding the equation of a straight line.

Equation of Lines!

We have:

$y=mx+b$y=mx+b  (gradient-intercept form)

$ay+bx-c=0$ay+bxc=0   (general form)

$y-y_1=m\left(x-x_1\right)$yy1=m(xx1)   (point-gradient formula)

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$yy1xx1=y2y1x2x1 (two point formula)

It's now time to practice using these different forms.

Worked Examples

QUESTION 1

A line has the equation $3x-y-4=0$3xy4=0.

1. Express the equation of the line in gradient-intercept form.

2. What is the gradient of the line?

3. What is the $y$y-value of the $y$y-intercept of the line?

QUESTION 2

A straight line passes through the point ($0$0, $\frac{3}{4}$34) with gradient $2$2.

1. Find the equation of the line in the form $y=mx+b$y=mx+b.

2. Express this equation in the general form $ax+by+c=0$ax+by+c=0.

3. Find the $x$x-intercept.

QUESTION 3

Consider the line with equation: $3x+y+2=0$3x+y+2=0

1. Solve for the $x$x-value of the $x$x-intercept of the line.

2. Solve for the $y$y-value of the $y$y-intercept of the line.

3. Plot the line.

QUESTION 4

1. Find the equation, in general form, of the line that passes through $A$A$\left(-12,-2\right)$(12,2) and $B$B$\left(-10,-7\right)$(10,7).

2. Find the $x$x-coordinate of the point of intersection of the line that goes through $A$A and $B$B, and the line $y=x-2$y=x2.

3. Hence find the $y$y-coordinate of the point of intersection.

Outcomes

NA6-7

Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns

91028

Investigate relationships between tables, equations and graphs