Question

A line has a slope of

1

3
and passes through the point (14,4). Write its equation in slope-intercept form.

Answer 1

The equation of the line with a slope of 1/3 passing through (14, 4) is y = ⅓x - 10 in slope-intercept form.

Step-by-step explanation:

To write the equation of a line with a slope of 1/3 that passes through the point (14, 4), we can use the point-slope form of a line equation:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the given values, we get y - 4 = ⅓(x - 14).

To convert this to slope-intercept form, y = mx + b, we need to solve for y by distributing the slope and moving the known y1 value to the other side of the equation.

Thus, the equation becomes y = ⅓x - ⅓(14) + 4, which simplifies to y = ⅓x - ⅓(42)/3 + 4, resulting in y = ⅓x - 14 + 4, or y = ⅓x - 10, which is the final equation in slope-intercept form.

Answer 2

To write the equation of a line with a slope of 1/3 and passing through the point (14,4) in slope-intercept form, use the point-slope form and simplify.

Step-by-step explanation:

To write the equation of a line in slope-intercept form (y = mx + b), we need to know the slope (m) and the y-intercept (b). In this case, the slope is 1/3, and the line passes through the point (14,4).

We can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get y - 4 = (1/3)(x - 14).

Next, we can simplify the equation by distributing the 1/3 to the terms in the parentheses, resulting in y - 4 = (1/3)x - 14/3. Finally, we can isolate y by adding 4 to both sides of the equation, giving us the final slope-intercept form: y = (1/3)x - 14/3 + 4.