All categories

3 years ago

Find the equation of a line parallel to y - 5x = 10 that passes through the point (3, 10). (answer in slope-intercept form)

Mathematics

2 answers:

MariettaO [177]3 years ago

8 0

Answer:

Step-by-step explanation:

NeX [460]3 years ago

6 0

So, a line parallel to y - 5x = 10, will have the same slope as that equation, so what is that slope anyway? let's solve for "y".

 $\bf y-5x=10\implies y=5x+10\implies y=\stackrel{slope}{5}x\stackrel{y-intercept}{+10}$

alrite, so the slope is 5 then, well, then the parallel line will have the same slope.

so, we're really looking for the equation of a line whose slope is 5 and runs through 3,10.

 $\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 3}}\quad ,&{{ 10}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 5
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-10=5(x-3)
\\\\\\
y-10=5x-15\implies y=5x-5$

You might be interested in

Not good with fractions can you help me out here. 8y =5

Sedbober [7]

Answer:

y=5/8

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Which describes the cross section of a square prism that passes through vertices A, B, and C?

expeople1 [14]

Answer:

In triangle ABC one side equal $8\sqrt{2}$ and two sides equal $4\sqrt{13}$

Step-by-step explanation:

We are given a prism whose base is square with sides 8 in and height 12 in.

If we take cross section through vertices A, B and C

We will get a cross section as triangle.

In triangle ABC, sides are AB, BC and AC

AB is diagonal of top square whose side 8 in.

$AB=\sqrt{8^2+8^2}=8\sqrt{2}$

AC is face diagonal of front face.

$AC=\sqrt{8^2+12^2}=4\sqrt{13}$

BC is face diagonal of right face.

$BC=\sqrt{8^2+12^2}=4\sqrt{13}$

AC=BC≠AB

Hence, In triangle ABC one side equal $8\sqrt{2}$ and two side equal $4\sqrt{13}$

6 0

3 years ago

Read 2 more answers

May someone help me with this problem please? thanks anyways.

lyudmila [28]

Answer:that is very hard never have done that yet

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

An 8 inch pizza is cut into 4 equal slices. A 10 inch pizza is cut into 6 equal slices.

salantis [7]

The 8 inch one
8/4=2
10/6= approx 1.66666666666666

5 0

4 years ago

Read 2 more answers

Write these as a product

Oxana [17]

Answer

${(2b - 5)}^{2} - 36 =( 2b - 11)(2b + 1)$

$9 - {(7 + 3a)}^{2} = (3a - 4)(3a + 11)$

$( {4 - 11m)}^{2} - 1 =( 3 - 11m )( 5 - 11m )$

Explanation

a) The given expresion is

${(2b - 5)}^{2} - 36$

We rewrite as difference of two squares

${(2b - 5)}^{2} - 36 = {(2b - 5)}^{2} - {6}^{2}$

Recall that:

${x}^{2} - {y}^{2} = (x + y)(x - y)$

This implies that:

${(2b - 5)}^{2} - 36 =( {(2b - 5)} -6)(2b - 5 )+ 6)$

${(2b - 5)}^{2} - 36 =( 2b - 5-6)(2b - 5 + 6)$

This simplifies to give:

${(2b - 5)}^{2} - 36 =( 2b - 11)(2b + 1)$

b) The second expression is

$9 - {(7 + 3a)}^{2}$

We rewrite as perfect squares yo get:

$9 - {(7 + 3a)}^{2} = {3}^{2} - {(7 + 3a)}^{2}$

This gives:

$9 - {(7 + 3a)}^{2} = ({3} - {(7 + 3a)})({3} + {(7 + 3a)})$

This implies that

$9 - {(7 + 3a)}^{2} = ({3} - 7 + 3a)({3} + 7 + 3a)$

We simplify to get:

$9 - {(7 + 3a)}^{2} = (3a - 4)(3a + 11)$

c) The third expression is:

$( {4 - 11m)}^{2} - 1$

We obtain the difference of two squares as:

$( {4 - 11m)}^{2} - 1 =( ( {4 - 11m)} - 1 )( ( {4 - 11m)} + 1 )$

We simplify within the parenthesis to get:

$( {4 - 11m)}^{2} - 1 =( 4 - 11m - 1 )( 4 - 11m+ 1 )$

We simplify further to get;

$( {4 - 11m)}^{2} - 1 =( 3 - 11m )( 5 - 11m )$

4 0

3 years ago