2.1 Homework
Question $9,2.1.47$,
HW Score: $77.06\mathrm{\%}$,
Points: 0 of 1
Find the slope-intercept form for the line passing through $(2,3)$ and parallel to the line passing through $(3,9)$ and $(-7,5)$.
The slope-intercept form for the line passing through $(2,3)$ and parallel to the line passing through $(3,9)$ and $(-7,5)$ is $y=$ (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Step 1 ：First, we need to find the slope of the line passing through $(3,9)$ and $(-7,5)$. The slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $m=\frac{y_2-y_1}{x_2-x_1}$.

Step 2 ：Using the formula, we find that the slope $m=0.4$.

Step 3 ：Next, we need to find the equation of the line parallel to it passing through $(2,3)$. The equation of a line in slope-intercept form is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

Step 4 ：Since the line we're looking for is parallel to the line passing through $(3,9)$ and $(-7,5)$, it will have the same slope. We can find $b$ by substituting the coordinates of the point $(2,3)$ into the equation and solving for $b$.

Step 5 ：We find that the y-intercept $b=2.2$.

Step 6 ：Therefore, the equation of the line in slope-intercept form is $y=0.4x+2.2$.

Step 7 ：$\boxed{{\displaystyle y=0.4x+2.2}}$ is the final answer.