Question

In the figure, if line $l$ has a slope of $-2$, what is the $y$-intercept of $l$?

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

Answer: (D)

$10$

In Slope-intercept form,

Equation of the straight line is $y$ $=$ $mx$ $+$ $c$

where, ${}^{\prime }{m}^{\prime }$ is the slope of the line

${}^{\prime }{c}^{\prime }$ is the y-intercept

Here, given that

slope of the line $=$ $-2$

$\Rightarrow m$ $=$ $-2$

From the figure, we can see that $(3,$ $4)$ is a point on the line.

By substituting the above in the equation of straight line, we get the y-intercept.

$m$ $=$ $-2$, $x$ $=$ $3$ and $y$ $=$ $4$

$\therefore y$ $=$ $mx$ $+$ $c$

$\therefore 4$ $=$ $(-2)$$\left(3\right)$ $+$ $c$

$\therefore 4$ $-$ $(-6)$ $=$ $c$

$\therefore c$ $=$ $10$

Therefore, the $y$ intercept of the line $l$ is $10$.