Question

write an equation in slope-intercept form of the line that passes through the p
(0, 1) and (4, 2) are marked on the line in the coordinate grid.
y = \square

Explanation:

Step1: Recall slope-intercept form

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

Step2: Find the y - intercept ($b$)

The y - intercept is the value of $y$ when $x = 0$. From the point $(0,1)$, we can see that when $x = 0$, $y=1$. So, $b = 1$.

Step3: Calculate the slope ($m$)

The formula for slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We have two points $(0,1)$ and $(4,2)$. Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(4,2)$. Then $m=\frac{2 - 1}{4 - 0}=\frac{1}{4}$.

Step4: Write the equation

Substitute $m=\frac{1}{4}$ and $b = 1$ into the slope - intercept form $y=mx + b$. We get $y=\frac{1}{4}x+1$.

Answer:

$\frac{1}{4}x + 1$