Question 152·Easy·Algebra

If a line passes through $(0,7)$, what does that tell you about the y-intercept $b$ in the equation $y = mx + b$?

You know the slope is $-4$ and the y-intercept is 7. Plug these into $y = mx + b$, then see which option matches that equation.

In four separate lines, type y = 7x - 4, y = -4x + 7, y = -7x + 4, and y = 4x - 7 so you can see all four lines on the same coordinate plane.

Click or tap on the point where each line crosses the y-axis (where $x=0$). Look at the y-coordinate and see which line has a point at $(0,7)$.

For the line that passes through $(0,7)$, pick two points on that line (for example, where $x=0$ and where $x=1$) and see how $y$ changes when $x$ increases by 1. The correct graph will have $y$ decrease by 4 when $x$ increases by 1, showing a slope of $-4$; match that graph to its equation from the choices.

A linear function can be written in slope-intercept form as

where $m$ is the slope and $b$ is the y-intercept (the value of $y$ when $x=0$). Since $g$ is linear, it can be written this way.

The graph passes through $(0,7)$. On a graph, the point with $x=0$ lies on the y-axis, so its $y$-value is the y-intercept.

That means $b = 7$, so the function has the form

We are told the slope of $g$ is $-4$. In the equation $y = mx + b$, the slope is $m$, the coefficient of $x$. Substitute $m=-4$ and $b=7$ into $y = mx + b$ to obtain the equation; we will express it in function notation and select the matching choice in the next step.

We find that the equation is $y = -4x + 7$, which in function notation is $g(x) = -4x + 7$. Among the choices, this corresponds to option B.