Finding Slope of a Line
Identify the slope of the following equation.
y = 3x - 2
the slope is 3
What form (Equation) do we use to graph a linear equation?
the slope-intercept form y = mx + b
Evaluate:
-2 - 5
-7
What form of equations do we use for lines?
y = mx + b or slope intercept form.
How do you write something in Point Slope Form?
What is the point slope equation?
y-y1=m(x-x1)
What is the standard Form of a linear equation?
Ax+By=C
Identify the slope of the following two points:
(3, -5) (-1, -2)
slope is -2 + 5 = 3 = -3/4
-1 -3 -4When graphing linear equations, where do we begin?
We begin at the y-intercept, b in the equation y=mx+ b.
Solve for x:
3x - 2 = -14
x = -4
Write an equation for a vertical line through the point (-3, 3)
x = -3
Write the equation in point slope form of a line that passes through the given point and has the given slope
(1,2) m=-4
Point Slope Form: y-2=-4(x-1)
Find the X intercept of the following Equation:
x+3y=-3
X=-3
Name three ways to describe slope.
Hint: definitions, equations, variables, etc
Possible answers:
rate of change
rise over run
y - y/x - x
slope = m in y = mx + b
Graph the following equation. Include at least 3 points. y = 1/3x + 4
Graph should start with the point at (0, 4) Movement should be 1 up and 3 to the right continuing to another point. Movement could also be 1 down and 3 to the left.
(3, 5)
(6, 6)
What is the slope of this equation?
x = 5
Undefined Slope
Write an equation for a line with the following slope and points.
m = 2/3 and (0, -2), (3, 0)
y = 2/3x - 2
Write the equation in point slope form:
(-1,-4); =-2
y+4=-2(x+1)
or
y-(-4)=-2(x-(-1))
Find the Y intercept of the following equation:
2x - y = 8
y = - 8
Find the slope of the line that includes the following points. (4, -5) (-4, 5)
-10/8 which simplifies to -5/4
Graph the following equation. Include at least three points. y = -3
Graph should begin with a point on the y-axis at -3. A horizontal line should be drawn through -3 extending on both sides of the y-axis.
Graph the following equation. 8x + 4y = 16
Rewrite in SLOPE Intercept Form First
(SHOW WORK on the white board and graph on the back)
Should be rewritten as y = -2x + 4 and then graphed.
Write an equation for a line with the following two points. Find the slope and y intercept. (15, -10) (5, 10)
m = 10 + 10/ 5 - 15 20/-10 = -2
Point Slope Form y - 10 = -2(x - 5)
y = -2x + 10 + 10
y = -2x + 20
y intercept = 20
Write the linear equation of a point that goes through (4,8) with a slope of m=3/4
Point Slope Form First then change to Slope Intercept
Point Slope: y - 8 = 3/4(x - 4)
y = 3/4x - 3 + 8
Slope Intercept Form: y=3/4x+5
Find the X and Y intercepts:
15x - 12y = 60
x= (4,0) or 4
y= (0,5) or 5
Find the slope of the line that includes the following points. (-12, -9) (-3, -3)
-6/-9 = 6/9 = 2/3
Graph y = 1/2x - 5 Then plot 3 ordered pairs on the line. Draw a line through the points. Label the ordered pairs on the line.
Graph the line starting at -5 on the y intercept. Rise 1, run 2. Draw the line. Label 3 points on the line.
Is x = 2 a solution to the equation 2(x - 5) + 3 = 13 ?
2(2 - 5) + 3 = 2(-3) + 3 = -6 + 3 = -3
No 2 it is not a solution.
The amount y(in dollars) of money you have left after playing x games at a carnival is y = -0.75x + 10. How much money do you have after playing eight games? Graph the equation and show your explanation.
y = -0.75(8) + 10
y = -6 + 10
y = 4 $4 dollars left after playing 8 games. Graph should begin at (0, 10) on the y-axis and move down three and four to the right.
Write the Linear Equation (y=mx+b) based on the 2 points: (2,4) and (3,6)
m = 6 - 4/3 - 2 = 2/1 = 2
Point Slope y - 4= 2(x - 2)
y = 2x - 4 + 4
Slope Intercept Form y=2x or y = 2x + 0
You have $6 to spend on apples and bananas. The standard form equation 1.5x + .6y = 6 represents this situation, where x is the number of pounds of apples and y in the number of pounds of bananas. Find the x and y intercepts (__, 0) and (0,__)
x=4 or (4,0)
y=10 or (0,10)