Answer:
To write the equation of a line in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, you can use the given slope and point.
For Question 5:
Given slope \(m = 1\) and point \((-2, 3)\).
Using the point-slope form: \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the given point.
Plugging in the values:
\(y - 3 = 1(x - (-2))\)
\(y - 3 = x + 2\)
\(y = x + 5\)
So, the equation of the line with slope 1 that contains the point (-2, 3) in slope-intercept form is \(y = x + 5\).
For Question 6:
Given slope \(m = 3\) and point \((-1, 6)\).
Using the point-slope form:
\(y - y_1 = m(x - x_1)\)
Plugging in the values:
\(y - 6 = 3(x - (-1))\)
\(y - 6 = 3(x + 1)\)
\(y - 6 = 3x + 3\)
\(y = 3x + 9\)
So, the equation of the line with slope 3 that contains the point (-1, 6) in slope-intercept form is \(y = 3x + 9\).
Answer:
y = x + 5 , y = 3x + 9
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 )
(5)
given slope m = 1 , then
y = x + c ← is the partial equation
to find c, substitute (- 2, 3 ) for x and y in the partial equation
3 = - 2 + c ( add 2 to both sides )
5 = c
y = x + 5 ← equation of line
(6)
given slope m = 3 , then
y = 3x + c ← is the partial equation
to find c, substitute (- 1, 6 ) for x and y in the partial equation
6 = 3(- 1) + c = - 3 + c ( add 3 to both sides )
9 = c
y = 3x + 9 ← equation of line
