Writing an Equation Given Two Points (3.10.2)

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 of a line given any two points on the line. If you have the point where x = 0, that is the y-intercept. So the y-value from that point is b.
First calculate the slope: m = –½. Substitute into the equation: y = –½x + b. Substitute the intercept: y = –½x + 3. Remember: Keep the coordinates for each point in the same column in the slope formula. In this example, 3 from (0, 3) is in the 2nd position, so 0 of (0, 3) is also. This habit keeps your signs correct. You’re done. Sometimes you have two points but neither of them is the y-intercept. First calculate your slope. In this case m = 3. Substitute 3 for m in the slope-intercept form. Now choose either of your points and substitute its values in for x and y so you can solve for b. In this case you get –1. Substitute the –1 in for b. You’re done.

Answer 6

You can create the equation of a line given any two points on the line. If you have the point where x = 0, that is the y-intercept. So the y-value from that point is b.
First calculate the slope: m = –½. Substitute into the equation: y = –½x + b. Substitute the intercept: y = –½x + 3. Remember: Keep the coordinates for each point in the same column in the slope formula. In this example, 3 from (0, 3) is in the 2nd position, so 0 of (0, 3) is also. This habit keeps your signs correct. You’re done. Sometimes you have two points but neither of them is the y-intercept. First calculate your slope. In this case m = 3. Substitute 3 for m in the slope-intercept form. Now choose either of your points and substitute its values in for x and y so you can solve for b. In this case you get –1. Substitute the –1 in for b. You’re done.