EOC - Unit 1 Practice Slope Intercept Form Example
What is an equation in slope-intercept form for the line that passes through the points (1, 3) and (3, 1)? Substitute the two given points into the slope formula to find the slope of the line.
2 2 Then substitute the slope and the coordinates of one of the points into the slope intercept form to find b. y = mx + b 3 = 2(1) + b 5 = b Use slope-intercept form. Substitute 2 for m, 1 for x, and 3 for y. Solve for b. Substitute the slope and y-intercept into the slope-intercept form. y = mx + b y = 2x + ( 5) Use slope-intercept form. Substitute 2 for m and 5 for b.
Point-Slope Form Example
A line passes through (5, –2) and has a slope –3. What is an equation for this line in point-slope form? y – y1 = m(x – x1) Use point-slope form. y – ( – 2) = – 3(x – 5) Substitute (5, – 2) for (x1, y1) and – 3 for m. y + 2 = – 3(x – 5) Simplify. A line passes through (1,4) and (2,9). What is an equation for this line in point-slope form? What is an equation for this line in slope-intercept form? First use the two given points to find the slope
1 5 Use the slope and one point to write an in point-slope form? y – y1 = m(x – x1) y – 4 = 5(x – 1) y – 4 = 5x – 5 y = 5x – 1 Use point-slope form Substitute (1, 4) for (x1, y1) and 5 for m. Distributive Property Add 4 to each side. An equation in point-slope form is y – 4 = 5(x – 1). An equation in slope-intercept form is y = 5x – 1.
The Standard Form Example
of a linear equation is
By = C
re real numbers, and
are not both zero. You can easily determine the
-intercepts of the graph from this form of the equation.
Each intercept occurs when one coordinate is 0. When substituting 0 for either of
, one of the terms on the left side of the standard form equation disappears. This leaves a linear equation in one variable, with a variable term on the left and a constant on the right. Determining the other coordinate of the intercept requires only multiplication or division.
What are the
-intercepts of the graph of 6
= 18 ? First find the x-intercept. 6x – 9y = 18 6
– 9(0) = 18 6
= 3 Substitute 0 for
Divide each side by 6.
Then find the y-intercept. 6x – 9y = 18 6(0) – 9y = 18 –9y = 18 y = –2 Substitute 0 for x. Simplify. Divide each side by –9. The x-intercept is 3 and the y-intercept is –2.
Parallel and Perpendicular Lines
Two lines that are neither horizontal nor vertical are perpendicular if the product of their slopes is 21. The graphs of and are perpendicular because x = -1
What is an equation in slope-intercept form of the line that passes through (2, 11) and is perpendicular to the graph of ? The slope of is Since the slope of the line perpendicular to the given line is –4. Use this slope and the given point to write an equation in point-slope form. Then solve for
to write the equation in slope-intercept form. Step 1. y – y1 = m(x – x1) Start with the point-slope form Step 2. Step 3. y – 11 = (–4x –2) y – 11 = –4x + 8 Substitute (2, 11) for (x1, y1) and –4 for m. Distributive Property Step 4. y = –4x + 19 Add 11 to each side. The graph of
+ 19 passes through (2, 11) and is perpendicular to the graph of
Practice Problems: (4 points each)
1. Hudson is already 40 miles away from home on his drive back to college. He is driving 65 mi/h. Write an equation that models the total distance
hours. What is the graph of the equation? 2. When Phil started his new job, he owed the company $65 for his uniforms. He is earning $13 per hour. The cost of his uniforms is withheld from his earnings. Write an equation that models the total money he has
hours of work. What is the graph of the equation? 3. A sign says that 3 tickets cost $22.50 and that 7 tickets cost $52.50. Write an equation in point-slope form 4. 5. that represents the cost of tickets. What is the graph of the equation? You have only nickels and dimes in your piggy bank. When you ran the coins through a change counter, it indicated you have 595 cents. Write and graph an equation that represents this situation. What are three combinations of nickels and dimes you could have?
On a map, Sandusky St. passes through coordinates (2, 1) and (4, 8). Pennsylvania Ave. intersects Sandusky St. and passes through coordinates (1, 3) and (6, 2). Are these streets perpendicular? Explain.