Answer:
y = 4x + 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x + 7 ← is in slope- intercept form
with slope m = 4
• Parallel lines have equal slopes , then
y = 4x + c ← is the partial equation
to find c substitute (- 3, 2 ) into the partial equation
2 = - 12 + c ⇒ c = 2 + 12 = 14
y = 4x + 14 ← equation of parallel line
Answer:
[tex]\boldsymbol{y=4x+14}[/tex]
Step-by-step explanation:
Hi student! Let me help you out on this question.
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First of all we need to find, the slope of the line that is parallel to the line [tex]\boldsymbol{y=4x+7}[/tex]. Which is pretty easy, considering the fact that the slopes of parallel lines are the same.
The slope of the line [tex]\boldsymbol{y=4x+7}[/tex] is [tex]\boldsymbol 4[/tex].
Which means the slope of the line that is parallel to the one above is also 4.
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Now we should find the equation of the line. We know that its slope is 4, so let's stick in 4 for the slope into the slope-intercept form equation:
(remember, m denotes the slope and b denotes the y intercept).
[tex]\boldsymbol{y=mx+b}[/tex]
Stick in 4 for the slope.
[tex]\boldsymbol{y=4x+b}[/tex]
Note that we are also given a point that's on the line.
We can stick in its y-co-ordinate, 2. for y.
[tex]\boldsymbol{2=4x+b}[/tex]
Now let's stick in -3 for x.
[tex]\boldsymbol{2=4(-3)+b}[/tex]
Solve for b.
[tex]\boldsymbol{2=-12+b}[/tex]
Add 12 to both sides.
[tex]\boldsymbol{2+12=b}[/tex]
[tex]\boldsymbol{14=b}[/tex]
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Now that we know the y-intercept, let's stick it into the slope-intercept form equation for b:
[tex]\boldsymbol{y=4x+14}[/tex]. Which is our final answer, the equation.
⇨Hope that this helped you out! Have a nice day ahead.⇦
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