Math With AmarA C A D E M Y

Grade 9 · Interpret signed slope and intercept · 205 of 750

Interpret signed slope and intercept · practice 19

For the line y = -1x + (7), find y when x = 3 and identify the slope and vertical intercept. Follow the calculation, then test the quantities in the animated example.

Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.

01 · Make a prediction

Your practice question

For the line y = -1x + (7), find y when x = 3 and identify the slope and vertical intercept.

Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.

02 · Explore the model

See the mathematical relationship move.

Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.

Watch the relationship

Paused
Interpret signed slope and intercept · practice 19. Moving input x: -5. Output y: 12. Slope: -1. Intercept: 7y = -1x + (7)-8-4048-40040xRead numeric axes; drawing scales differ.
Inputs and outputs are abstract real quantities with no unstated context restrictions. Axes use different drawing scales; the fixed window is x∈[−8,8], y∈[−40,40]. A line continues beyond the clipped window.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Moving input x
-5
Output y
12
Slope
-1
Intercept
7

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

The mathematical idea

In y=mx+b, the slope describes output change per input unit and the intercept gives the output at zero. Changing b translates a graph while leaving its rate unchanged. A negative slope means output decreases as input increases; zero slope gives a constant function. Starting quantities: Slope m = -1; Intercept b = 7.

y = mx + b; Δy/Δx = m

03 · Reflect and transfer

Explain what changes and why.

Can two different lines share the same value at x = 3? Explain.

This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.