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Graphing Linear Functions in Slope-Intercept Form

Graphing Linear Functions in Slope-Intercept Form 1.7 - Solution

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a

The function rule is written in slope-intercept form, y=mx+b.y=mx+b. First we want to identify the line's slope, m,m, and yy-intercept, b.b. y=3x9m=3 and b=-9 y={\color{#0000FF}{3}}x {\color{#009600}{-9}} \quad \quad \quad m={\color{#0000FF}{3}} \text{ and } b={\color{#009600}{\text{-} 9}} We can see that the yy-intercept is b=-9.b=\text{-} 9. Therefore, the graph crosses the yy-axis at (0,-9).(0,\text{-} 9). The slope, m,m, is 3.3. This means that the line increases by 33 units in the yy-direction while moving 11 unit to the right in the xx-direction. Using this we can find two points on the line.

We can draw the graph of the function by connecting the points with a line.

We can now with words describe what this graph looks like. When moving 11 unit to the right, the line increases by 33 units. The line crosses the yy-axis at y=-9.y=\text{-}9.

b

We need to find the line's slope and yy-intercept. For a line written in slope-intercept form, y=mx+b,y=mx+b, the slope is mm and the yy-intercept is b.b. y=-2x+5m=-2 and b=5 y={\color{#0000FF}{\text{-}2}}x+{\color{#009600}{5}} \quad \quad \quad m={\color{#0000FF}{\text{-}2}} \text{ and } b={\color{#009600}{5}} We have a yy-intercept of b=5.b=5. This means that the function crosses the yy-axis when y=5.y = 5. The slope is -2,\text{-}2, which means that the line decreases by 22 units in the yy-direction while moving 11 unit to the right in the xx-direction. We can use this to find two points on the graph.

Let's draw the graph of the function. We do that by connecting the points with a line.

We are ready to describe what the graph looks like. When moving 11 unit to the right, the line decreases by 22 units. The line crosses the yy-axis at y=5.y=5.