Respuesta :
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y-4=1/4(x-8). The slope-intercept form of the equation for this line is y = x/4 + 2.
The equation of the line in the point-slope form :
y - b = m(x - a)
where m is the slope and (a,b) are the points on the line.
y - 4 = (x - 8)/4
Here, m = 1/4 and (a,b) = (8,4)
The equation of the line in slope-intercept form:
y = mx +c
y = x/4 + c
To find c, putting (8,4) into the above equation,
4 = 2 + c
c = 2
Therefore, y = x/4 + 2 is the slope-intercept form.
What is the intercept?
- The point where the line or curve crosses the axis of the graph is called the intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.
- An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.
- X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.
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