Writing an Equation in Slope-Intercept Form (3.10.1)

Question 1

• Standard equation of a line: Ax + By = C. A linear equation will always have an x to the first power, a y, and some constant.

Answer 1

• Standard equation of a line: Ax + By = C. A linear equation will always have an x to the first power, a y, and some constant.

Question 2

• Slope-intercept equation of a line: y = mx + b. The constant, m, represents the slope or rate of change from one point to the next in the line. The constant, b, represents the y-intercept or point where the line crosses the y-axis.

Answer 2

• Slope-intercept equation of a line: y = mx + b. The constant, m, represents the slope or rate of change from one point to the next in the line. The constant, b, represents the y-intercept or point where the line crosses the y-axis.

Question 3

• The y-intercept is the point where the line crosses the y-axis. The x-value is always 0. The y-value is represented by the variable b. The point’s coordinates are (0, b).

Answer 3

• The y-intercept is the point where the line crosses the y-axis. The x-value is always 0. The y-value is represented by the variable b. The point’s coordinates are (0, b).

Question 4

• It is often very useful to express an equation that is given in standard form in slope-intercept form.

Answer 4

• It is often very useful to express an equation that is given in standard form in slope-intercept form.

Question 5

• To change a standard equation to a slope-intercept equation solve the equation for y.

Answer 5

• To change a standard equation to a slope-intercept equation solve the equation for y.

Question 6

You can create the equation for a line if you know the
y-intercept and its slope. Start with: y = mx + b. Substitute your slope, –2, in for m. Substitute your y-intercept, 5, in for b. You’re done. Same thing works in this example: Start with: y = mx + b. Substitute ½ for m: y = ½ x + b. Substitute –6 for b: y = ½ x –6. You’re done. You can also use the slope-intercept form of an equation to create a graph of the line. Start with the equation: y = –2/3x + 1. Place the y-intercept: (0, 1). Use the slope: count down –2 and to the right 3. Place a point at that location. Draw the line through the two points. The same process works here. Start with the equation: y = ½ x –3. Place the y-intercept: (0, –3). Use the slope: count up 1 and to the right 2. Place a point at that location. Draw the line through the two points. Many people will suggest doing at least three points to reduce the possibility of error.

Answer 6

You can create the equation for a line if you know the
y-intercept and its slope. Start with: y = mx + b. Substitute your slope, –2, in for m. Substitute your y-intercept, 5, in for b. You’re done. Same thing works in this example: Start with: y = mx + b. Substitute ½ for m: y = ½ x + b. Substitute –6 for b: y = ½ x –6. You’re done. You can also use the slope-intercept form of an equation to create a graph of the line. Start with the equation: y = –2/3x + 1. Place the y-intercept: (0, 1). Use the slope: count down –2 and to the right 3. Place a point at that location. Draw the line through the two points. The same process works here. Start with the equation: y = ½ x –3. Place the y-intercept: (0, –3). Use the slope: count up 1 and to the right 2. Place a point at that location. Draw the line through the two points. Many people will suggest doing at least three points to reduce the possibility of error.