Find the slope and y-intercept of the line with the given equation. (a) 7x + y = =6 m =U; (0,O) (b) x + 9y = -18 D; (0, m = (c) -10x – 2y = 7 ; (0, m =

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Find the slope and y-intercept of the line with the given equation.
(a) 8x + y = 9 (b)x+ 4y
3D 16 (с) —9х — Зу %3D 11
We will write each equation in slope-intercept form, y = mx + b.
When the equations are written in slope-intercept form, the slope and y-intercept
of their graphs become apparent.
(a) The slope and y-intercept of the graph of 8x + y = 9 are not obvious because the equation is not in
slope-intercept form. To write it in y = mx + b form, we isolate y on left side.
8х + у %3D 9
8х + у — 8х %3D —8х +
To eliminate the term 8x on the left side, subtract 8x from both sides.
y =
x + 9
On the left side, combine like terms: 8x – 8x = 0.
у3 —8х + 9
↑
m = -8 ↑
b =
The slope is -8.
The y-intercept is (0, 9).
(b) To write the equation in slope-intercept form, we solve for y.
x + 4y = 16
x + 4y
- X
-X +
To eliminate the x term on the left side, subtract x from both sides.
4y = -x +
Simplify the left side.
4y
-x + 16
To isolate y,
undo the multiplication by 4 by dividing both sides by 4.
4
-X
+
4
On the right side, write (-x+16)/4 as the sum of two fractions with
like denominators.
y =
4
1
х +
4
y =
Write -x/4 as (-1/4)x. Simplify: 16/4 = 4.
-
and b = 4, the slope is
4
and the y-intercept is (0, 4).
Since m = -
Transcribed Image Text:Find the slope and y-intercept of the line with the given equation. (a) 8x + y = 9 (b)x+ 4y 3D 16 (с) —9х — Зу %3D 11 We will write each equation in slope-intercept form, y = mx + b. When the equations are written in slope-intercept form, the slope and y-intercept of their graphs become apparent. (a) The slope and y-intercept of the graph of 8x + y = 9 are not obvious because the equation is not in slope-intercept form. To write it in y = mx + b form, we isolate y on left side. 8х + у %3D 9 8х + у — 8х %3D —8х + To eliminate the term 8x on the left side, subtract 8x from both sides. y = x + 9 On the left side, combine like terms: 8x – 8x = 0. у3 —8х + 9 ↑ m = -8 ↑ b = The slope is -8. The y-intercept is (0, 9). (b) To write the equation in slope-intercept form, we solve for y. x + 4y = 16 x + 4y - X -X + To eliminate the x term on the left side, subtract x from both sides. 4y = -x + Simplify the left side. 4y -x + 16 To isolate y, undo the multiplication by 4 by dividing both sides by 4. 4 -X + 4 On the right side, write (-x+16)/4 as the sum of two fractions with like denominators. y = 4 1 х + 4 y = Write -x/4 as (-1/4)x. Simplify: 16/4 = 4. - and b = 4, the slope is 4 and the y-intercept is (0, 4). Since m = -
(c) To write the equation in y = mx + b form, we isolate y on the left side.
— 9х — Зу %3D 11
-
у 3D 9х + 11
To eliminate the term –9x on the left side, add 9x to both sides: -9x + 9x = 0.
9x
+
-3
-3y
To undo the multiplication by –3, divide both sides by -3.
%3D
-3
3
у3 —Зх —
Simplify.
Since m = -3 and b =
11
the slopes is -3 and the y-intercept is
Find the slope and y-intercept of the line with the given equation.
(а) 7х + у %3D-6
m =; (0,
(b) x + 9y = -18
; (0,
m =
(с) —10х — 2у %3D 7
m = D; (0, O)
Transcribed Image Text:(c) To write the equation in y = mx + b form, we isolate y on the left side. — 9х — Зу %3D 11 - у 3D 9х + 11 To eliminate the term –9x on the left side, add 9x to both sides: -9x + 9x = 0. 9x + -3 -3y To undo the multiplication by –3, divide both sides by -3. %3D -3 3 у3 —Зх — Simplify. Since m = -3 and b = 11 the slopes is -3 and the y-intercept is Find the slope and y-intercept of the line with the given equation. (а) 7х + у %3D-6 m =; (0, (b) x + 9y = -18 ; (0, m = (с) —10х — 2у %3D 7 m = D; (0, O)
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