Part 1 of 4 Use the graph of the line shown. a. Write a point-slope form of the equation for the line shown. b. Estimate the value of the \( y \)-intercept of the line. c. Use proportional reaconimg to eumpar your conjecture about the value of the \( y \)-intercept. d. Rewrite the point-slope form of the equation in slope-intercept form to check your conjecture. a. A point-sloge form of the equation for the line shown is \( \square \) (Type an equation)

To write a point-slope form of the equation for the line shown, you'll need a point on the line and the slope. Let's say the line passes through the point \((x_1, y_1)\) and has a slope \(m\). The point-slope form equation would look like this: \(y - y_1 = m(x - x_1)\) Now, just plug in your values for \(x_1\), \(y_1\), and \(m\) to fill in that \( \square \)! To estimate the \( y \)-intercept, check where the line intersects the \( y \)-axis (where \( x = 0 \)). This point gives you the value of \( b \) in the slope-intercept form \( y = mx + b \). Your \( y \)-intercept might look something like this: \( \hat{b} \) if you want to note it down! And for proportional reasoning, if you've spotted two points on the line that you can clearly see, you can create ratios involving their coordinates to get a sense of the changes. This can lead you closer to estimating that \( y \)-intercept visually. Finally, to convert to slope-intercept form, solve the point-slope equation for \( y \) to see it in this shape: \(y = mx + b\) Remember to adjust your \( b \) value based on that conjecture and check how close it is to your estimate from before! Happy calculating!