Finding Slope
Use the table below to find the slope of the line passing through the points.
slope = (9-5)/(4-2) = 4/2 = 2
Write an equation for a line with a slope of 2 and a y-intercept of -5.
y = 2x - 5
Maria buys 3 notebooks and 2 pens for $11. Each notebook costs $2 and each pen costs p dollars. Write and solve an equation to find the cost of one pen.
Equation: 3 times 2 + 2p = 11
Solution: p = 2.5
Write the equation in standard form for a line with a slope of 3 and a y-intercept of -2.
Slope intercept Form Equation: y = 3x - 2
Standard form equation solution: -3x + y = -2
Find the slope of the line that passes through the points (3, 7) and (6, 13).
Slope = (13-7)/(6-3) = 6/3 = 2
Solve for x in the equation: 3x + 7 = 19.
3x + 7 - 7 = 19 - 7
3x = 12
3/3 x = 12/3
x = 4
A school is selling tickets for a play. On the first day, they sold 5 adult tickets and 6 student tickets for a total of $64. If each adult ticket costs $8, write and solve an equation to find the cost of each student ticket.
Equation: 5 times 8 + 6s = 64
Solution: s = 4
Rewrite the equation y = -2x + 7 in standard form and solve for y when x = 4.
Standard form: 2x+ y = 7
Solution: -1
Use the two labeled points to find the slope.
Point A at (1,2), Point B at (5,6)
Slope (6-2)/(5-1) = 4/4 = 1
A line has a slope of -3 and passes through the point (2, 4). Write the equation for the line in slope-intercept form.
y - 4 = -3(x - 2)
y - 4 = -3x + 6
y - 4 + 4 = -3x + 6 + 4
y = -3x + 10
A soccer team scored a total of 22 goals in two games. They scored 6 more goals in the first game than in the second. Write and solve an equation to find out how many goals they scored in each game.
Let x be the number of goals in the second game.
Equation: x + (x + 6) = 22
Solution: First game: 14, Second game: 8
Given the points (1, 5) and (4, 11).
Find the slope m of the line that passes through these points.
(11- 5) / (4 -1) = 6/3 = 2
Find the slope between the points (0, -3) and (4, 5).
Slope = (5- -3)/(4-0) = 8/4 = 2
The table shows the relationship between x and y. Write the linear equation that represents this relationship.
slope = 4/2 = 2
y-int = 4
y = 2x + 4
Given the points (1, 5) and (4, 11).
Write the equation of the line in point-slope form using one of the points. Rearrange your equation into standard form Ax + By = C.
y-5 = 2(x-1)
y-5 = 2x-2
Standard form -2x + y = 3
A line goes through (1, 4) and (3, 8). What is its slope?
Slope = (8-4)/(3-1) = 4/2 = 2
Solve for y in the equation: 5y - 2 = 18.
5y - 2 + 2 = 18 + 2
5y = 20
5/5 y = 20/5
y = 4
Standard form -2x + y = 3
Identify the values of A, B, and C in your final equation.
A = -2, B = 1, C = 3