Question

function a and function b are linear functions.
function a
(graph of a line on a coordinate plane with x from -10 to 10 and y from -10 to 10. the line passes through (0, -2) and (8, 10))
function b
$y = \frac{3}{4}x - 5$
select all the statements that are true.

• the y-intercept of function a is less than the y-intercept of function b.
• the y-intercept of function a is greater than the y-intercept of function b.
• the y-value of function a when x = 8 is equal to the y-value of function b when x = 8.
• the y-value of function a when x = 8 is greater than the y-value of function b when x = 8.

Explanation:

Step1: Find y - intercept of Function A

From the graph of Function A, when \(x = 0\), \(y=- 2\). So the y - intercept of Function A is \(-2\).

Step2: Find y - intercept of Function B

The equation of Function B is \(y = \frac{3}{4}x-5\). For a linear function in the form \(y=mx + b\), the y - intercept is \(b\). So the y - intercept of Function B is \(-5\).
Compare \(-2\) and \(-5\): Since \(-2>-5\), the y - intercept of Function A is greater than the y - intercept of Function B.

Step3: Find y - value of Function A at \(x = 8\)

From the graph of Function A, when \(x = 8\), looking at the graph, the point is \((8,10)\), so \(y = 10\).

Step4: Find y - value of Function B at \(x = 8\)

Substitute \(x = 8\) into \(y=\frac{3}{4}x - 5\). \(y=\frac{3}{4}\times8-5=6 - 5=1\).
Compare \(10\) and \(1\): Since \(10>1\), the y - value of Function A when \(x = 8\) is greater than the y - value of Function B when \(x = 8\).

Answer:

• The \(y\) - intercept of Function A is greater than the \(y\) - intercept of Function B.
• The \(y\) - value of Function A when \(x = 8\) is greater than the \(y\) - value of Function B when \(x = 8\).