Find the equation of the line that satisfies the given conditions.
(a) Write the equation in standard form.
(b) Write the equation in slope-intercept form.
x-intercept (1,0); slope 2
The standard form of the eauation is....?
The slope-intercept form of the equation is y=....?
Explanation and answers?
We have a slope (2) and a point (1, 0)
We could use something known as the point - slope equation to get to the slope-intercept form, but here's a faster way. Note that, if the slope is 2, this means that everytime x changes by a positive 1, y changes by a positive 2. And everytime x changes by a negative 1, y changes by a negative 2. So, when x changes from 1 to 0, it changes by a negative 1, so y changes by negative 2.... from 0 to -2. So (0, -2) is on the graph...so the y intercept is at -2.
So......the slope intercept form is given by:
y = mx + b where m is the slope and b is the y intercept. So we have
y = 2x - 2 and that's slope-intercept form
To get standard form, get x and y on one side of the equation and the constant on the other
So we have (noting that y = 1y)
y = 2x - 2 or 1y = 2x - 2 subtract 1y from both sides and add 2 to both sides....so we have,,,
2 = 2x - 1y or 2x - 1y = 2 and that's standard form
We have a slope (2) and a point (1, 0)
We could use something known as the point - slope equation to get to the slope-intercept form, but here's a faster way. Note that, if the slope is 2, this means that everytime x changes by a positive 1, y changes by a positive 2. And everytime x changes by a negative 1, y changes by a negative 2. So, when x changes from 1 to 0, it changes by a negative 1, so y changes by negative 2.... from 0 to -2. So (0, -2) is on the graph...so the y intercept is at -2.
So......the slope intercept form is given by:
y = mx + b where m is the slope and b is the y intercept. So we have
y = 2x - 2 and that's slope-intercept form
To get standard form, get x and y on one side of the equation and the constant on the other
So we have (noting that y = 1y)
y = 2x - 2 or 1y = 2x - 2 subtract 1y from both sides and add 2 to both sides....so we have,,,
2 = 2x - 1y or 2x - 1y = 2 and that's standard form