Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of each equation.
1. (3,2), y=x + 5
2.(4,-6),y=-3/4x + 1
3.(-8,2),5x-4y=1
Could you guy check if these are the answer?
1.y=x-1
2.y=-3/4x -3
3.y=5/4x + 12
Thanks
good job
A quick way to see if you were right would have been to sub in the given point in your new equation.
If it satisfies, you're ok.
That is how I checked your equations.
Could do use one of mine and show me how you check it? Thanks
last one,
point (-8,2) , your equation y = (5/4)x + 12
Left side
= y
= 2
Right side
= (5/4)x + 12
= (5/4)(-8) + 12
= -40/4 + 12
= -10 + 12
= 2
Left side = Right side,
everything is good.
To find the slope-intercept form of an equation of a line that is parallel to a given line and passes through a given point, we need to follow these steps:
1. Find the slope of the given line.
2. Use the given point and the slope to form the equation.
Let's go through each case:
1. The given equation is y = x + 5, and the point is (3, 2).
Step 1: The given equation is in slope-intercept form y = mx + b, where the slope (m) is the coefficient of x. In this case, the slope is 1.
Step 2: Now that we have the slope of the given line, we can use it with the given point to form the equation. Using the point-slope form y - y1 = m(x - x1) and substituting the values, we get:
y - 2 = 1(x - 3)
Simplifying:
y - 2 = x - 3
Adding 2 to both sides:
y = x - 1
So the equation of the line that passes through (3, 2) and is parallel to the graph y = x + 5 is y = x - 1.
2. The given equation is y = -3/4x + 1, and the point is (4, -6).
Step 1: The slope of the given line is already provided, -3/4.
Step 2: Using the point-slope form, we get:
y - (-6) = -3/4(x - 4)
Simplifying:
y + 6 = -3/4x + 3
Subtracting 6 from both sides:
y = -3/4x - 3
So the equation of the line that passes through (4, -6) and is parallel to the graph y = -3/4x + 1 is y = -3/4x - 3.
3. The given equation is 5x - 4y = 1, and the point is (-8, 2).
Step 1: We need to rearrange the given equation into the slope-intercept form, y = mx + b.
Starting with 5x - 4y = 1, we isolate y:
-4y = -5x + 1
Dividing both sides by -4:
y = 5/4x - 1/4
Now we can determine the slope, which is 5/4.
Step 2: Using the point-slope form:
y - 2 = (5/4)(x - (-8))
y - 2 = (5/4)(x + 8)
Simplifying:
y - 2 = 5/4x + 10
Subtracting 2 from both sides:
y = 5/4x + 12
So the equation of the line that passes through (-8, 2) and is parallel to the graph 5x - 4y = 1 is y = 5/4x + 12.
Your answers are correct!