Question

function a and function b are linear functions.
function a
function b
complete the sentences.
the slope of function a is the slope of function b. the y - intercept of
function a is the y - intercept of function b.

Explanation:

Step1: Find slope of Function A

Two points on Function A: \((-8, 0)\) and \((0, 2)\). Slope formula: \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So \(m_A=\frac{2 - 0}{0 - (-8)}=\frac{2}{8}=\frac{1}{4}\).

Step2: Find slope of Function B

Two points on Function B: \((0, -3)\) (wait, looking at graph, maybe \((0, -3)\)? Wait, no, let's recheck. Wait, Function B: when \(x = 0\), \(y=-3\)? Wait, no, maybe points \((4, 0)\) and \((0, -3)\)? Wait, no, let's take two clear points. From graph, Function B: when \(x = 4\), \(y = 0\); when \(x = 0\), \(y=-3\)? Wait, no, maybe I misread. Wait, the line for Function B: let's see, when \(x = 0\), \(y=-3\)? Wait, no, maybe the y-intercept is -3? Wait, no, looking at the grid, Function B: let's take two points. Let's see, when \(x = 4\), \(y = 0\); when \(x = 0\), \(y=-3\)? Wait, no, maybe the slope is \(\frac{3}{4}\)? Wait, no, let's recalculate. Wait, Function A: points \((-8, 0)\) and \((0, 2)\), so slope \(m_A=\frac{2 - 0}{0 - (-8)}=\frac{2}{8}=\frac{1}{4}\). Function B: let's take points \((0, -3)\) and \((4, 0)\). Then slope \(m_B=\frac{0 - (-3)}{4 - 0}=\frac{3}{4}\)? Wait, no, maybe I made a mistake. Wait, the graph of Function B: when \(x = 0\), \(y=-3\)? Wait, no, looking at the right graph, the line crosses y-axis at -3? Wait, no, the y-axis is vertical. Wait, maybe the y-intercept of Function B is -3? Wait, no, maybe the points are \((0, -3)\) and \((4, 0)\), so slope \(m_B=\frac{0 - (-3)}{4 - 0}=\frac{3}{4}\). Wait, but \(\frac{1}{4}<\frac{3}{4}\), so slope of A is less than slope of B.

Step3: Find y-intercept of Function A

Y-intercept is when \(x = 0\), so \(y = 2\) for Function A.

Step4: Find y-intercept of Function B

Y-intercept is when \(x = 0\), so \(y=-3\) (wait, no, maybe I misread. Wait, the right graph: the line for Function B, when \(x = 0\), \(y=-3\)? Wait, no, looking at the grid, the y-axis is from -8 to 8. Wait, maybe the y-intercept of Function B is -3? Wait, no, maybe the line is \(y=\frac{1}{2}x - 3\)? Wait, no, let's take two points. Let's see, when \(x = 4\), \(y = -1\)? No, I think I messed up. Wait, let's re-express. Wait, Function A: slope \(\frac{1}{4}\), y-intercept 2. Function B: let's take two points: (0, -3) and (4, 0). So slope is \(\frac{0 - (-3)}{4 - 0}=\frac{3}{4}\). So slope of A (\(\frac{1}{4}\)) is less than slope of B (\(\frac{3}{4}\)). Y-intercept of A is 2, y-intercept of B is -3? Wait, no, that can't be. Wait, maybe the y-intercept of Function B is -3? Wait, no, looking at the right graph, the line is going up, so when x increases, y increases. So when x = 0, y is negative. So y-intercept of B is negative, y-intercept of A is positive (2). So y-intercept of A (2) is greater than y-intercept of B (which is -3). Wait, but maybe I misread the y-intercept of B. Wait, let's check the graph again. The right graph: the line crosses the y-axis at -3? Wait, no, the grid lines: each square is 1 unit. So the y-axis: from -8 to 8, each grid is 1. So Function B: when x = 0, y is at -3? Wait, no, the line is yellow, and at x = 0, it's at -3? Wait, no, maybe the y-intercept is -3, and slope is \(\frac{3}{4}\). So slope of A is \(\frac{1}{4}\), slope of B is \(\frac{3}{4}\), so slope of A is less than slope of B. Y-intercept of A is 2, y-intercept of B is -3, so y-intercept of A is greater than y-intercept of B.

Step5: Compare slopes and y-intercepts

Slope of A (\(\frac{1}{4}\)) < Slope of B (let's say \(\frac{3}{4}\)). Y-intercept of A (2) > Y-intercept of B (let's say -3).

Answer:

The slope of Function A is less than the slope of Function B. The y - intercept of Function A is greater than the y - intercept of Function B.

So first blank: less than; second blank: greater than.