Question

Write a linear equation that does not intersect the graph of y=-2x+3 and has an x-intercept of 1. Explain your reasoning.

Answer 1

`\\ewline{\text{The equaiton of the line is y=-2x+2}}`

Explanation:

`\\ewline{\text{If 2 lines to not intersect, then those 2 lines are paralell.}}`
`\bigskip\\ewline{\text{Also, the x-intercept is where the line crosses the x axis or where y=0.}}`
`\bigskip\\ewline{\text{We need to find 2 lines that are paralell and have an x intercept of 1}}`
`\bigskip\bigskip\\ewilne{\text{Paralell lines have the same slope}}`
`\bigskip\\ewline{\text{For y=mx+b, m is the slope}}`
`\bigskip\\ewline{\text{Since our original equation was y=-2x+3, the slope is -2}}`
`\bigskip\\ewline{\text{Paralell lines have same slope so our mystery line is y=-2x+b where b is a constant}}`
`\bigskip\\ewline{\text{To find the value of b, we can use the 'point' given by the x-intercept}}`
`\bigskip\\ewline{\text{x-intercept of 1 means that when y=0, x=1, so (1,0) is a point that is true}}`
`\bigskip\\ewline{\text{Find the value of b that makes y=-2x+b true for (1,0)}}\bigskip\\ewline{\text{Subsitute 1 for x and 0 for y}}\bigskip\\ewline{0=-2(1)+b}\bigskip\\ewline{0=-2+b}`
`\bigskip\\ewline{2=b}\bigskip\bigskip\\ewline{\text{The equation of the line is y=-2x+2}}`

Answer 2

y =-2x+2

Explanation:

We want a line that does not intersect y = -2x+3

It must be parallel to this line, so it must have the same slope (Parallel lines have the same slope)

The slope is -2

We have an x intercept of 1 (1,0)

The have the slope and a point

We can use the point slope form of a line to write the equation

y-y1 = m(x-x1)

y-0 = -2(x-1)

Distribute

y=-2x+2

y =-2x+2

This is in slope intercept form