Question

Which of the following is an equation in slope-intercept form for the line shown?

F$y=\frac{1}{4}x-1$

G$y=\frac{1}{4}x+4$

H$y=4x-1$

J$y=4x+4$

Short answer

Theoption (F) is correct. The equation of the straight line is $y=\frac{x}{4}-1$.

Step-by-step solution

Step 1. State the concept of the slope-intercept form of an equation.

The slope-intercept form of a linear equation is $y=mx+b$, where $m$ is the slope and $b$is the $y$-intercept.

Step 2. Write the equation in the intercept form. 

From the graph, the $x$-intercept is 4 while the $y$-intercept is $-1$.

Write the equation in the intercept form,

$\frac{x}{4}+\frac{y}{\left(-1\right)}=1$

Step 3. Write the equation of a line in slope-intercept form.

Convert this equation in slope and intercept form by separating them $y$from the equation in the intercept form.

$$\begin{gathered} \frac{x}{4}-y=1 \\ y=\frac{x}{4}-1 \end{gathered}$$

Therefore, option (F) is correct. The equation of the straight line is $y=\frac{x}{4}-1$.