Question

What type of lines are these? Y = 2x + 4 and 2y = -4x + 10

Answer 1

ANSWER

The lines are two intersecting lines. They intersect` at the point $(\frac{1}{4}, \frac{9}{2})$

EXPLANATION

To determine which type of lines, we look for the slopes of the two lines and compare them to see whether they are parallel or perpendicular.

The first line is $y=2x+4--(1)$.

This line is already in the form;

$y=mx+c$, which is referred to as the slope intercept form, where $m=2$ is the slope.

The second line is

$2y=-4x+10$

Dividing through by 2 gives;

$y=-2x+5--(2)$

This implies that, this line also has a slope of $-2$.

Since the two slopes are not the same,the lines are not parallel.

Also the the product of the two slopes, $-2\times 2 \ne -1$, hence the two lines are  not perpendicular.

Adding equation (1) and (2) gives;

$2y=9$

$\Rightarrow y=4.5$

Putting $y=4.5$ in  equation (1) gives

$4.5=2x+4$

$\Rightarrow 0.5=2x$

$\Rightarrow x=\frac{1}{4}$.

Hence the two lines intersect` at the point $(\frac{1}{4}, \frac{9}{2})$