Question

1. Use point-slope form to write the equation of a line that has a slope of 2/3 and passes through (-3, -1). Write your final equation in slope-intercept form.

2. Write the equation in standard form using integers (no fractions or decimals): 𝑦 = −2/3𝑥 − 1

3. Write an equation of the line that passes through (2, -1) and is parallel to the graph of y = 5x – 2. Write your final equation in slope-intercept form.

4. Write an equation of the line that passes through(3, 5) and is perpendicular to the graph of y = –3x +7. Write your final equation in slope-intercept form.

5. Sketch a graph y = |x – 3| – 2 and describe the translations.

Answer 1

I am not going to do all your work for you.
I will start number 4
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4. Write an equation of the line that passes through(3, 5) and is perpendicular to the graph of y = –3x +7. Write your final equation in slope-intercept form.
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what is the slope of a line perpendicular to y = -3x + 7 ????
well m = -3
the slope of a perpendicular = -1/m = -(1/-3)= 1/3
so we have
y = (1/3) x + b
what is b ????
well we havea point (3,5)
so
5 =(1/3)(3) + b
5 = 1 + b
b= 4
so in the end
y = (1/3) x + 4