Question

Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.

Answer 1

Answer:

$y = -2x + 5$

m = -1

b = 5

Step-by-step explanation:

Hello!

Slope - Intercept Form: $y = mx+b$

• m = slope
• b = y-intercept

Slope

The slope of the line is the rate of change, or how the graph changes in y as it changes in x.

Slope can be calculated by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).

Calculate Slope

• $m = \frac{y_2 - y_1}{x_2 - x_1}$
• $m = \frac{5 - (-3)}{0 - 4}$
• $m = -\frac{8}{4}$
• $m = -2$

The slope is -2.

Y-intercept

The y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.

The intersection happens at point (0,5), so the y-intercept is 5.

Equation

We found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.

Equation: $y = -2x + 5$