the coordinate plane and equations of lines\nwriting the equation of a line given the y-intercept and…

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at $(0, 3)$, so $b = 3$.

Step2: Identify another point

The line passes through the point $(-5, 7)$.

Step3: Calculate the slope

Using $m = \frac{y_2 - y_1}{x_2 - x_1}$: $$m = \frac{7 - 3}{-5 - 0} = \frac{4}{-5} = -\frac{4}{5}$$

Step4: Write the equation

Substitute $m$ and $b$ into $y = mx + b$: $$y = -\frac{4}{5}x + 3$$

Answer:

y = -\frac{4}{5}x + 3