Write an equation of the line through the point (5, 3) that is perpendicular to the line –3x+7y=5.
2 answers:
Answer:
7x + 3y = 44
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c (m is the slope and c the y- intercept )
Rearrange - 3x + 7y = 5 into this form by adding 3x to both sides
7y = 3x + 5 ( divide all terms by 7 )
y = x +
← in slope- intercept form
with slope m =
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= -
, thus
y = - x + c ← is the partial equation
To find c substitute (5, 3) into the partial equation
3 = - + c ⇒ c = 3 +
=
y = - x +
← in slope- intercept form
Multiply through by 3
3y = - 7x + 44 ( add 7x to both sides )
7x + 3y = 44 ← in standard form
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Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
, thus, the equation is:
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,
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
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4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
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Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3
The second line, through (1, 1) and (2, -1) is the purple line.
Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
The equation of the second line can be found as follows:
the slope is
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3
Answer:
∠A = 84°
Step-by-step explanation:
Since AB and AC are tangent to the circle, ∠ABK = 90° and ∠ACK = 90°.
Angles of a quadrilateral add up to 360°, so:
∠A + 90° + 90° + 96° = 360°
∠A = 84°
