Writing Linear Equations in Slope-Intercept Form

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Presentation transcript:

Writing Linear Equations in Slope-Intercept Form

Quick Review An equation of a line can be written in slope- intercept form y = mx + b where m is the slope and b is the y- intercept. The y-intercept is where a line crosses the y- axis.

Writing an Equation of a Line Suppose the slope of a line is 5 and the y- intercept is 2. How would this you write the equation of this line in slope-intercept form? First write the slope-intercept form. y = mx + b Now substitute 5 for m and 2 for b. y = 5x + 2

Write the Equation of a Line from a Graph Where does the line cross the y-axis? At the point (0, -4) The y-intercept is -4. What is the slope of the line? The graph also crosses the x-axis at (2, 0). We can use the slope formula to find our slope. m = -4 – 0 = -4 = 2 0 – 2 -2 We know our slope is 2 and our y-intercept is -4, what is the equation of our line? y = mx + b y = 2x + (-4) y = 2x -4

Let’s try an example! Write the equation of a line with a slope of -2 and a y-intercept of 6. y = mx + b y = -2x + 6

Using a graph Where does the line cross the y-axis? At the point (0, 2) So the y-intercept b is 2. The line also passes through the point (3, 0). We can use these points to find the slope of the line. How? What formula do we use? Using the slope formula, we find that the slope m is -2/3. Write the equation of the line. y= mx + b y = (-2/3)x + 2

If we are given the Slope and a Point Step 1: First find the y-intercept. Substitute the slope m and the coordinates of the given point (x, y) into the slope-intercept form, y = mx + b. Then solve for the y-intercept b. Step 2: Then write the equation of the line. Substitute the slope m and the y-intercept b into the slope- intercept form, y = mx + b.

If We Are Given the Slope and a Point Suppose we have a slope of -3 and it passes through the point (1, 2). We first need to find the y-intercept. We can do this by substituting our information into slope-intercept form and solving for b. y = mx + b 2 = -3(1) + b 2 = -3 + b Add 3 to both sides. 5 = b Now we know that the y-intercept is 5. y = -3x + 5

Try This! Suppose we have a line with a slope of -1 and passes through the point (3, 4). y = mx + b 4 = (-1)3 + b 4 = -3 + b 7 = b y = (-1)x + 7 y = -x + 7