Question

which statement comparing the graph and the equation is true?
( y = -2x + 7 )
the graph has a greater slope than the equation.
the graph and the equation have the same slope.
the graph and the equation have the same ( y )-intercept.
the graph has a greater ( y )-intercept than the equation.

Explanation:

Step1: Find graph's slope

Pick two points on $f(x)$: $(0,2)$ and $(4,0)$. Slope formula: $\frac{y_2-y_1}{x_2-x_1} = \frac{0-2}{4-0} = -\frac{1}{2}$

Step2: Identify equation's slope

Equation $y=-3x+7$ is in $y=mx+b$ form, so slope $m=-3$

Step3: Compare y-intercepts

Graph crosses y-axis at $(0,2)$, so y-intercept=2. Equation's y-intercept $b=7$

Step4: Evaluate each option

• Slope of graph $(-0.5) >$ slope of equation $(-3)$: this is true.
• Slopes are not equal: false.
• Y-intercepts (2 vs 7) not equal: false.
• Graph's y-intercept (2) < equation's (7): false.

Answer:

The graph has a greater slope than the equation.