A line passes through the point (3,7) and (6,8) then find the slope of the line.
Answers
Answer:
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Step-by-step explanation:
Point slope form:
y
−
7
=
3
4
(
x
−
3
)
Slope intercept form:
y
=
3
4
x
+
19
4
.
.
or
.
.
y
=
3
4
x
+
4
3
4
Explanation:
Since you have one point and the slope, you can use the point slope formula, then solve for
y
to get the slope intercept form, so that you can determine the y-intercept
(
b
)
. Then you can graph the resulting equation.
Point slope formula
y
−
y
1
=
m
(
x
−
x
1
)
, where
x
1
,
y
1
=
(
3
,
7
)
, and
m
=
3
4
is the slope.
Substitute the given values into the formula.
y
−
7
=
3
4
(
x
−
3
)
Expand.
y
−
7
=
3
4
x
−
9
4
Solve for
y
to get the slope intercept form:
y
=
m
x
+
b
, where
m
=
3
4
is the slope and
b
is the y-intercept.
y
−
7
=
3
4
x
−
9
4
Add
7
to both sides.
y
−
7
+
7
=
3
4
x
−
9
4
+
7
Simplify.
y
=
3
4
x
−
9
4
+
7
In order to add and subtract fractions, they must have the same denominator.
7
=
7
1
and can be multiplied by the equivalent fraction
4
4
in order to get the same denominator as
9
4
.
y
=
3
4
x
−
9
4
+
7
1
×
4
4
Simplify.
y
=
3
4
x
−
9
4
+
28
4
Simplify.
y
=
3
4
x
+
19
4
or
y
=
3
4
x
+
4
3
4
The y-intercept is
19
4
graph{y=3/4x+19/4 [-17.42, 14.6, -5.96, 10.06]}